Question

line segment ba is tangent to the circle. what is the length of line segment ba? round to the nearest unit. 18 units 65 units 88 units 98 units

Explanation:

Step1: Apply tangent - secant rule

If a tangent and a secant are drawn to a circle from an exterior point, then the square of the length of the tangent is equal to the product of the lengths of the secant and its external segment. Let the length of the tangent \(BA = x\), the secant \(BD=120\) and the external - part of the secant \(BC = 35\). Then \(x^{2}=BC\times BD\).

Step2: Calculate the value of \(x^{2}\)

\(x^{2}=35\times120 = 4200\).

Step3: Find the value of \(x\)

\(x=\sqrt{4200}\approx64.8\approx65\) (rounded to the nearest unit).

Answer:

C. 65 units